The goal of combinatorial materials discovery is to find compositions of matter that maximize a specific material property, such as superconductivity, magnetoresistance, luminescence, ligand specificity, sensor response, or catalytic activity. (See, e.g., McFarland, E. W. and Weinberg, W. H. Combinatorial approaches to materials design. TIBTECH 17, 107-115 (1999); Pirrung, M. C. Spatially addressable combinatorial libraries. Chem. Rev. 97, 473-488 (1997); Weinberg, W. H., Jandeleit, B., Self, K. and Turner, H. Combinatorial methods in homogeneous and heterogeneous catalysis. Curr. Opin. Chem. Bio. 3, 104-110 (1998); Xiang, X.-D., Sun, X., Bricexc3x1o, G., Lou, Y., Wang, K.-A., Chang, H., Wallace-Freedman, W. G., Chang, S.-W. and Schultz, P. G. A combinatorial approach to materials discovery. Science 268, 1738-1740 (1995); Bricexc3x1o, G., Chang, H., Sun, X., Schultz, P. G. and Xiang, X.-D. A class of cobalt oxide magnetoresistance materials discovered with combinatorial synthesis. Science 270, 273-275 (1995); Danielson, E., Golden, J. H., McFarland, E. W., Reaves, C. M., Weinberg, W. H. and Wu, X. D. A combinatorial approach to the discovery and optimization of luminescent materials. Nature 389, 944-948 (1997); Danielson, E., Devermey, M., Giaquinta, D. M., Golden, J. H., Haushalter, R. C., McFarland, E. W., Poojary, D. M., Reaves, C. M., Weinberg, W. H. and Wu, X. D. A rare-earth phosphor containing one-dimensional chains identified through combinatorial methods. Science 279, 837-839 (1988); Wang, J., Yoo, Y., Gao, C., Takeuchi, L, Sun, X., Chang, H., Xiang, X.-D. and Schultz, P. G. Identification of a blue photoluminescent composite material from a combinatorial library. Science 279, 1712-1714 (1998); Burger, M. T. and Still, W. C. Synthetic ionophores, encoded combinatorial libraries of cyclen-based receptors for Cu2+ and Co2+. J. Org. Chem. 60, 7382-7383 (1995); Liu, G. and Ellman, J. A. A general solid-phase synthesis strategy for the preparation of 2-pyrrolidinemethanol ligands. J. Org. Chem. 60, 7712-7713 (1995); Bilbertson, S. R. and Wang, X. The combinatorial synthesis of chiral phosphine ligands. Tetrahed. Lett. 37, 6475-6478 (1996); Francis, M. B., Jamison, T. F. and Jacobsen, E. N. Combinatorial libraries of transition-metal complexes, catalysts and materials. Curr. Opin. Chem. Biol. 2, 422-428 (1998); Dickinson, T. A. and Walt, D. R. Generating sensor diversity through combinatorial polymer synthesis. Anal. Chem. 69, 3413-3418 (1997); Menger, F. M., Eliseev, A. V. and Migulin, V. A. Phosphatase catalysis developed via combinatorial organic chemistry. J. Org. Chem. 60, 6666-6667 (1995); Burgess, K., Lim, H.-J., Porte, A. M. and Sulikowski, G. A. New catalysts and conditions for a Cxe2x80x94H insertion reaction identified by high throughput catalyst screening. Angew. Chem. Int. Ed. 357 220-222 (1996); Cole, B. M., Shimizu, K. D., Krueger, C. A., Harrity, J. P. A., Snapper, M. L. Hoveyda, A. H. Discovery of chiral catalysts through ligand diversity: Ti-catalyzed enantioselective addition of TMSCN to meso epoxides. Angew. Chem. Int. Ed. 35, 1668-1671 (1996); Akporiaye, D. E., Dahl, I. M., Karlsson, A. and Wendelbo, R. Combinatorial approach to the hydrothermal synthesis of zeolites. Angew. Chem. Int. Ed. 37, 609-611 (1998); Reddington, E., Sapienza, A., Gurau, B., Viswanathan, R., Sarangapani, S., Smotkin, E. S. and Mallouk, T. E. Combinatorial electrochemistry: A highly parallel, optical screening method for discovery of better electrocatalysts. Science 280, 1735-1737 (1998); and Cong, P., Doolen, R. D., Fan, Q., Giaquinta, D. M., Guan, S., McFarland, E. W., Poojary, D. M., Self, K., Turber, H. W. and Weinberg, W. H. High-throughput synthesis and screening of combinatorial heterogeous catalyst libraries. Angew. Chem. Int. Ed. 38., 484-488 (1999)].
A variety of materials have been optimized or developed to date by combinatorial methods. Perhaps the first experiment to gather great attention was the demonstration that inorganic oxide high-Tc superconductors could be identified by combinatorial methods (Xiang et al., supra). By searching several 128-member libraries of different inorganic oxide systems, the known compositions of superconducting BiSrCaCuO and YBaCuO were identified. Since then, many demonstrations of finding known materials and discoveries of new materials have appeared. Known compositions of magnetoresistant materials have been identified in libraries of various cobalt oxides (Bricexc3x1o et al., supra). Blue and red phosphors have been identified from large libraries of 25,000 different inorganic oxides [Danielson et al. (1998), supra; Danielson et al. (1988), supra; and Wang et al., supra]. Polymer-based sensors for various organic vapors have been identified by combinatorial methods (Dickinson et al., supra). Catalysts for the oxidation of CO to CO2 have been identified by searching ternary compounds of Pd, Pt, and Rh or Rh, Pd, and Cu (Pirrung, supra, and Cole et al., supra). Phase diagrams of zeolitic materials have been mapped out by a combinatorial xe2x80x9cmultiautoclavexe2x80x9d (Akporiaye et al., supra). Novel enantioselective catalysts have been found by searching libraries of transition metal-peptide complexes (Cole et al., supra). Novel phosphatase catalysts were found by searching libraries of carboxylic acid-functionalized polyallylamime polymers (Menger et al., supra). New catalysts and conditions for Cxe2x80x94H insertion have been found by screening of ligand-transition metal systems (Burgess et al., supra). A new catalyst for the conversion of methanol in a direct methanol fuel cell was identified by searching the quaternary composition space of Pt, Ir, Os, and Ru (Reddington et al., supra). Finally, a novel thin-film high dielectric compound that may be used in future generations of DRAM chips was identified by searching through over 30 multicomponent, ternary oxide systems [van Dover, R. B., Schneemeyer, L. F. and Fleming, R. M. Discovery of a useful thin-film dielectric using a composition-spread approach. Nature 392, 162-164 (1998)].
Present approaches to combinatorial library design and screening invariably amount to a grid search in composition space, followed by a xe2x80x9csteepest-ascentxe2x80x9d maximization of the figure of merit. Such optimization procedures, however, are inefficient methods at finding optima in high-dimensional spaces or when the figure of merit is not a smooth function of the variables. Indeed, the use of a grid search is what has limited essentially all current combinatorial chemistry experiments to quaternary compounds, i.e., to searching a space with three variables. What is needed is an automated, yet more efficient, procedure for searching composition space.
The present invention uses Monte Carlo methods to provide just such a powerful new procedure for searching a multi-dimensional space of variables in combinatorial chemistry. Moreover, the effectiveness of the new protocols is validated on the Random Phase Volume Model, showing the new methods to be superior to those in current practice.
The present invention provides a method for generating a combinatorial library, which begins by preparing a first set of current samples using a grid search or a random selection method. Preferably, each initial sample has at least one composition or non-composition variable selected by a random method. In one preferred Monte Carlo method, the first set of current samples is prepared by choosing the variables of each current sample at random from allowed values. Alternatively, the first set of current samples could be prepared by choosing the variables of each current sample via a quasi-random, low discrepancy sequence.
The next step is preparing a new set of proposed samples by changing the variables of each current sample by a Monte Carlo selection method. A preferred method for changing the variables is a random displacement protocol, which randomly changes at least one of the composition and non-composition variables of a randomly chosen current sample a small amount. The process continues until the variables of each sample of the set are changed. A swapping move, which trades a subset of the variables between at least one pair-of randomly chosen current samples, may also be included in the protocol.
The present invention further provides a method of performing multiple rounds of generating the aforementioned combinatorial libraries, which includes the additional feedback steps of determining a figure of merit for each current and proposed sample and forming a modified set of current samples according to an acceptance criterion derived from a detailed balance condition. If the figure of merit of a proposed sample is greater than the figure of merit of the current sample, then the proposed sample is accepted and replaces the current sample. If the figure of merit of the proposed sample is less than the figure of merit of the current sample, the proposed sample will be accepted according to a predetermined probability.
In a preferred version of the method, the acceptance criterion following a random displacement is a probability determined by a detailed balance formula, which in this case is simply the Metropolis formula:
p=min{1, exp[xcex2(Eproposedxe2x88x92Ecurrent)]},xe2x80x83xe2x80x83(1)
wherein the parameter xcex2 defines the scale of the variations of the figure of merit that are likely to be accepted, and E is the figure of merit.
In another preferred version of the method, the acceptance criterion of a swapping move, which swaps samples i and j in one subset is:
p=min{1, exp{xcex2[Eiproposed+Ejproposedxe2x88x92Eicurrentxe2x88x92Ejcurrent]}.xe2x80x83xe2x80x83(2)
Parallel tempering is a more powerful method of the present invention for searching the space of composition and non-composition variables. In parallel tempering, the samples are grouped into two or more subsets. During the rounds of combinatorial chemistry each subset is updated using a different Metropolis probability, e.g. by using different values for the parameter xcex2. The parallel tempering protocol includes an additional step of randomly exchanging two or more samples between the subsets. The exchange step is accepted with an acceptance criterion derived from a detailed balance condition.
The composition variables are preferably one or more mole fractions of an element or compound.
The non-composition variables can include film thickness, deposition method, guest composition, host composition, impurity level, temperature, pressure, pH, atmospheric composition, crystallinity, phase, morphology, method of nucleation, method of synthesis, and other processing variables.
The figure of merit typically measures a property, such as luminescence, catalytic activity or selectivity, superconductivity, giant or colossal magnetoresistance, dielectric screening, biological activity, binding affinity, or sensing ability.
The methods for generating and screening combinatorial libraries, outlined above, will typically be iterated for one or more rounds until a maximum figure of merit is obtained.
Other versions of the present invention include the combinatorial libraries generated according to the aforementioned protocols.
Yet another version of the present invention is directed to an apparatus for generating a combinatorial library. The apparatus typically includes: (a) one or more sample preparation robots to robotically prepare a first set of current samples and one or more new sets of proposed samples in accordance with a sample preparation protocol, whereby each sample has one or more variables that can be changed independently; (b) one or more analysis robots to robotically analyze each sample to determine a figure of merit; and (c) a robotic control device for generating a sample preparation protocol in accordance with the methods of the present invention.
The robotic control device will generally include: (1) a mechanism for selecting the variables to use in preparing the first set of current samples, wherein the variables are selected by either a grid search or a Monte Carlo method; and (2) a mechanism for selecting variables to use in preparing the new set of proposed samples, wherein the variables of each current sample are changed using a Monte Carlo selection method to give a proposed sample. In addition the device may include: (3) a mechanism for comparing the figure of merit of a proposed sample with the figure of merit of a current sample, wherein the variables of the current sample were changed to give the proposed sample; and (4) a mechanism for accepting a modified set of current samples, according to the detailed balance acceptance criterion, described above. In addition, the robotic control device may also include a mechanism to determine whether to continue with another round of proposed samples.